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OBJECTIVE - G.GPE.B.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

INTERPRETATION OF OBJECTIVE - G.GPE.B.6

This objective uses the term directed line segment which is really just a funny name for a vector. We use our dilation techniques here to partition a segment into two parts based on a given ratio.

SKILLS

(1) The student will be able to partition a line segment based on a provided ratio.

THE BIG IDEA

This objective connects slope and dilation together. I think the big idea here is simply using skills to solve problems using coordinates and coordinate skills.

TRAPS & PITFALLS

For the most part this isn't too difficult as long as they remember the things covered earlier in the year with dilations. The only real issue is to alter ratios from piece comparison (1:3) to scale factor (1/4). Dilation is based on amount of the whole whereas most ratios are provided comparing to each other.

PAST CONNECTIONS

The student needs to use a reduction dilation to be able to perform this objective which is an earlier objective. The concept of slope is also a very important foundational understanding here.

FUTURE CONNECTIONS

Ultimately this is about ratios and coordinates which do show up in different shapes and problems later on. This also bridges a student from 'directed line segments' to VECTORS.

MY REFLECTIONS (over line l)

I think I should just teach this right after dilations in unit #2. Students will still remember the connection between slope and dilation and then the only thing that they are adding is converting ratios to scale factors. While this does deal with coordinates and is included in this unit I think it fits best in unit #2.